An exact single-product factorisation of the molecular wave function for the timedependent Schr̈odinger equation is investigated by using an ansatz involving a phase factor. By using the Frenkel variational method, we obtain the Schr̈odinger equations for the electronic and nuclear wave functions. The concept of a potential energy surface (PES) is retained by introducing a modified Hamiltonian as suggested earlier by Cederbaum. The parameter ω in the phase factor is chosen such that the equations of motion retain the physically appealing Born– Oppenheimer-like form, and is therefore unique.